If you are draining into an open sink or tub, you don't have to have a vent or trap. The vent is to give stack gases a place to go and to keep your trap from siphoning dry. With no stack gases on the far end, there is no concern of this. If you hook into the sink below the its trap, you need the darkroom trap and, as mentioned, 'autovents' are the easiest.

Thanks Eric. Actually the idea is to just run a drain pipe over to the laundry tub and let the large darkroom sink drain into the tub from the top withought tieing into the plumbing per se. Im just curious if its going to drain properly without a vent stack on the line.

So long as you have sufficient drop (1/4-inch per foot of run for a 2-inch pipe), your darkroom sink should drain fine. I thought you would cut into the laundry sink drain below that sink to get the necessary drop, as the traps on both sinks would probably be about the same height. But it you can discharge into the top of the laundry sink and get enough drop, it will work fine without a vent. Based on what I have been taught over the years, I would not go smaller than 2-inch pipe, however I see John Powers used 1.5-inch and had no problems. The smaller the pipe, the more drop you’ll need for a satisfactory flow.

The drain and down spout from the Arkay sink I used was 1.5" OD. With that size at the start there would have been no point in going to a larger size pipe. My drop is 24" plus a slight grade built into the basement concrete floor. The 35' pipe goes right into the sump at the other end of the basement. With that drop the fluids come out as a torrent.